SIAM Journal on Optimization, Volume 30, Issue 2, Page 1049-1066, January 2020.
We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system. Our approach sheds new light on and connects several well-known condition measures for conic systems, including Renegar's distance to infeasibility, the Grassmannian condition measure, a measure of the most interior solution, and other geometric measures of symmetry and of depth of the conic system.

中文翻译：

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线性圆锥系统不可行的数据独立距离

SIAM优化杂志，第30卷，第2期，第1049-1066页，2020年1月。
我们对均匀圆锥系统的不同适定性度量进行统一处理。为此，我们完全基于定义圆锥系统的元素的几何考虑，引入了到不可行的距离。我们的方法为圆锥形系统提供了新的视角，并将其连接起来，包括几个著名的条件度量，包括Renegar到不可行的距离，格拉斯曼条件度量，最内部解的度量以及圆锥形系统的对称性和深度的其他几何度量。 。